Submission #974412

#TimeUsernameProblemLanguageResultExecution timeMemory
974412marvinthangStar Trek (CEOI20_startrek)C++17
100 / 100
56 ms17352 KiB
/************************************* * author: marvinthang * * created: 03.05.2024 16:12:22 * *************************************/ #include <bits/stdc++.h> using namespace std; #define fi first #define se second #define left ___left #define right ___right #define TIME (1.0 * clock() / CLOCKS_PER_SEC) #define MASK(i) (1LL << (i)) #define BIT(x, i) ((x) >> (i) & 1) #define __builtin_popcount __builtin_popcountll #define ALL(v) (v).begin(), (v).end() #define REP(i, n) for (int i = 0, _n = (n); i < _n; ++i) #define REPD(i, n) for (int i = (n); i-- > 0; ) #define FOR(i, a, b) for (int i = (a), _b = (b); i < _b; ++i) #define FORD(i, b, a) for (int i = (b), _a = (a); --i >= _a; ) #define FORE(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i) #define FORDE(i, b, a) for (int i = (b), _a = (a); i >= _a; --i) #define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u) #define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u) #ifdef LOCAL #include "debug.h" #else #define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); } #define DB(...) 23 #define db(...) 23 #define debug(...) 23 #endif template <class U, class V> scan_op(pair <U, V>) { return in >> u.first >> u.second; } template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; } template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.first << ", " << u.second << ')'; } template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); } template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); } template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; } const int MOD = 1e9 + 7; namespace MODULAR { inline void fasterLLDivMod(unsigned long long x, unsigned y, unsigned &out_d, unsigned &out_m) { unsigned xh = (unsigned)(x >> 32), xl = (unsigned)x, d, m; #ifdef __GNUC__ asm( "divl %4 \n\t" : "=a" (d), "=d" (m) : "d" (xh), "a" (xl), "r" (y) ); #else __asm { mov edx, dword ptr[xh]; mov eax, dword ptr[xl]; div dword ptr[y]; mov dword ptr[d], eax; mov dword ptr[m], edx; }; #endif out_d = d; out_m = m; } template <class T> T invGeneral(T a, T b) { a %= b; if (!a) return b == 1 ? 0 : -1; T x = invGeneral(b, a); return x == -1 ? -1 : ((1 - 1LL * b * x) / a + b) % b; } template <int MOD> struct ModInt { unsigned int val; ModInt(void): val(0) {} ModInt(const long long &x) { *this = x; } ModInt & normalize(const unsigned int &v) { val = v >= MOD ? v - MOD : v; return *this; } bool operator ! (void) { return !val; } ModInt & operator = (const ModInt &x) { val = x.val; return *this; } ModInt & operator = (const long long &x) { return normalize(x % MOD + MOD); } ModInt operator - (void) { return ModInt(MOD - val); } ModInt & operator += (const ModInt &other) { return normalize(val + other.val); } ModInt & operator -= (const ModInt &other) { return normalize(val + MOD - other.val); } ModInt & operator /= (const ModInt &other) { return *this *= other.inv(); } ModInt & operator *= (const ModInt &other) { unsigned dummy; fasterLLDivMod((unsigned long long) val * other.val, MOD, dummy, val); return *this; } ModInt operator + (const ModInt &other) const { return ModInt(*this) += other; } ModInt operator - (const ModInt &other) const { return ModInt(*this) -= other; } ModInt operator * (const ModInt &other) const { return ModInt(*this) *= other; } ModInt operator / (const ModInt &other) const { return ModInt(*this) /= other; } ModInt pow(long long n) const { assert(n >= 0); ModInt res = 1, a = *this; for (; n; n >>= 1, a *= a) if (n & 1) res *= a; return res; } ModInt inv(void) const { int i = invGeneral((int) val, MOD); assert(~i); return i; } ModInt & operator ++ (void) { return *this += 1; } ModInt & operator -- (void) { return *this -= 1; } ModInt operator ++ (int) { ModInt old = *this; operator ++(); return old; } ModInt operator -- (int) { ModInt old = *this; operator --(); return old; } friend ModInt operator + (const long long &x, const ModInt &y) { return ModInt(x) + y; } friend ModInt operator - (const long long &x, const ModInt &y) { return ModInt(x) - y; } friend ModInt operator * (const long long &x, const ModInt &y) { return ModInt(x) * y; } friend ModInt operator / (const long long &x, const ModInt &y) { return ModInt(x) / y; } friend ostream & operator << (ostream &out, const ModInt &x) { return out << x.val; } friend istream & operator >> (istream &in, ModInt &x) { long long a; in >> a; x = a; return in; } explicit operator bool(void) const { return val; } explicit operator int(void) const { return val; } }; using Modular = ModInt <MOD>; } using namespace MODULAR; template <class T> struct Matrix { int numRow, numCol; vector <T> val; // accessors typename vector<T>::iterator operator [] (int r) { return val.begin() + r * numCol; } inline T & at(int r, int c) { return val[r * numCol + c]; } inline T get(int r, int c) const { return val[r * numCol + c]; } // constructors Matrix() {} Matrix(int r, int c): numRow(r), numCol(c), val(r * c) {} Matrix(const vector <vector <T>> &d) { numRow = d.size(); numCol = numRow ? d[0].size() : 0; for (int i = 0; i < numRow; ++i) { assert((int) d[i].size() == numCol); copy(d[i].begin(), d[i].end(), back_inserter(val)); } } Matrix & set_value(T v) { for (int i = 0; i < numRow * numCol; ++i) val[i] = v; return *this; } // convert to 2D vector vector <vector <T>> vecvec(void) const { vector <vector <T>> res(numRow); for (int i = 0; i < numRow; ++i) copy(val.begin() + i * numCol, val.begin() + (i + 1) * numCol, back_inserter(res[i])); return res; } operator vector <vector <T>> () const { return vecvec(); } static Matrix identity(int n) { Matrix res(n, n); for (int i = 0; i < n; ++i) res.at(i, i) = T(1); return res; } friend istream & operator >> (istream &in, Matrix &res) { for (T &x: res.val) in >> x; return in; } friend ostream & operator << (ostream &out, const Matrix &res) { for (int i = 0; i < res.numRow * res.numCol; ++i) cout << res.val[i] << " \n"[i % res.numCol == res.numCol - 1]; return out; } Matrix operator - (void) { Matrix res(numRow, numCol); for (int i = 0; i < numRow * numCol; ++i) res.val[i] = -val[i]; return res; } Matrix operator * (const T &v) { Matrix res = *this; for (T &x: res.val) x *= v; return res; } Matrix operator / (const T &v) { Matrix res = *this; const T inv = T(1) / v; for (T &x: res.val) x *= inv; return res; } Matrix operator + (const Matrix &other) const { int M = numRow, N = numCol; assert(M == other.numRow); assert(N == other.numCol); Matrix res = *this; for (int i = 0; i < numRow * numCol; ++i) res.val[i] += other.val[i]; return res; } Matrix operator - (const Matrix &other) const { int M = numRow, N = numCol; assert(M == other.numRow); assert(N == other.numCol); Matrix res = *this; for (int i = 0; i < numRow * numCol; ++i) res.val[i] -= other.val[i]; return res; } Matrix operator * (const Matrix &other) const { int M = numRow, N = numCol, P = other.numCol; assert(N == other.numRow); Matrix t_other = other.transpose(); Matrix res(M, P); for (int i = 0; i < M; ++i) for (int j = 0; j < P; ++j) res.at(i, j) = inner_product(this->val.begin() + N * i, this->val.begin() + N * (i + 1), t_other.val.begin() + t_other.numCol * j, T(0)); return res; } Matrix & operator *= (const T &v) { return *this = *this * v; } Matrix & operator /= (const T &v) { return *this = *this / v; } Matrix & operator += (const Matrix &other) { return *this = *this + other; } Matrix & operator -= (const Matrix &other) { return *this = *this - other; } Matrix & operator *= (const Matrix &other) { return *this = *this * other; } Matrix pow(long long Exp) const { int M = numRow; assert(M == numCol); assert(Exp >= 0); Matrix res = identity(M); if (!Exp) return res; bool is_id = true; for (int i = 63 - __builtin_clzll(Exp); i >= 0; --i) { if (!is_id) res *= res; if (Exp >> i & 1) res *= *this, is_id = false; } return res; } Matrix transpose(void) const { Matrix res(numCol, numRow); for (int i = 0; i < numRow; ++i) for (int j = 0; j < numCol; ++j) res.at(j, i) = this->get(i, j); return res; } }; // end of template void process(void) { int n; long long d; cin >> n >> d; vector <vector <int>> adj(n); REP(i, n - 1) { int u, v; cin >> u >> v; --u; --v; adj[u].push_back(v); adj[v].push_back(u); } vector <int> cnt_lose(n), cnt_fw(n), cnt_fl(n), f(n); auto cal = [&] (int u) { if (cnt_lose[u] == 1) f[u] = cnt_fl[u]; else if (!cnt_lose[u]) f[u] = cnt_fw[u] + 1; else f[u] = 0; }; auto dfs = [&] (auto &&dfs, int u, int par) -> void{ for (int v: adj[u]) if (v != par) { dfs(dfs, v, u); cnt_lose[u] += !cnt_lose[v]; (cnt_lose[v] ? cnt_fw[u] : cnt_fl[u]) += f[v]; } cal(u); }; dfs(dfs, 0, 0); vector <int> g(n); vector <int> lst_win, lst_lose; auto dfs2 = [&] (auto &&dfs, int u, int par) -> void { (cnt_lose[u] ? lst_win : lst_lose).push_back(u); g[u] = f[u]; for (int v: adj[u]) if (v != par) { cnt_lose[u] -= !cnt_lose[v]; (cnt_lose[v] ? cnt_fw[u] : cnt_fl[u]) -= f[v]; cal(u); cnt_lose[v] += !cnt_lose[u]; (cnt_lose[u] ? cnt_fw[v] : cnt_fl[v]) += f[u]; cal(v); dfs(dfs, v, u); cnt_lose[v] -= !cnt_lose[u]; (cnt_lose[u] ? cnt_fw[v] : cnt_fl[v]) -= f[u]; cal(v); cnt_lose[u] += !cnt_lose[v]; (cnt_lose[v] ? cnt_fw[u] : cnt_fl[u]) += f[v]; cal(u); } }; dfs2(dfs2, 0, 0); Modular k; for (int u: lst_win) k += g[u]; for (int u: lst_lose) k -= g[u]; Matrix <Modular> base({{lst_lose.size(), 1LL * n * n}}); Matrix <Modular> trans({ {k, 0}, {lst_lose.size(), 1LL * n * n} }); base *= trans.pow(d - 1); cout << (cnt_lose[0] ? base[0][1] - g[0] * base[0][0] : g[0] * base[0][0]) << '\n'; } int main(void) { ios_base::sync_with_stdio(false); cin.tie(nullptr); // cout.tie(nullptr); file("startrek"); // int t; cin >> t; while (t--) process(); // cerr << "Time elapsed: " << TIME << " s.\n"; return (0^0); }

Compilation message (stderr)

startrek.cpp: In function 'void process()':
startrek.cpp:281:39: warning: narrowing conversion of 'lst_lose.std::vector<int>::size()' from 'std::vector<int>::size_type' {aka 'long unsigned int'} to 'long long int' [-Wnarrowing]
  281 |  Matrix <Modular> base({{lst_lose.size(), 1LL * n * n}});
      |                          ~~~~~~~~~~~~~^~
startrek.cpp:284:17: warning: narrowing conversion of 'lst_lose.std::vector<int>::size()' from 'std::vector<int>::size_type' {aka 'long unsigned int'} to 'long long int' [-Wnarrowing]
  284 |   {lst_lose.size(), 1LL * n * n}
      |    ~~~~~~~~~~~~~^~
startrek.cpp: In function 'int main()':
startrek.cpp:30:61: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   30 |     #define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
      |                                                      ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
startrek.cpp:292:2: note: in expansion of macro 'file'
  292 |  file("startrek");
      |  ^~~~
startrek.cpp:30:94: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   30 |     #define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
      |                                                                                       ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
startrek.cpp:292:2: note: in expansion of macro 'file'
  292 |  file("startrek");
      |  ^~~~
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